A lot depends on the kind of horse you're talking about. If you're talking QH or the saddle-type breeds, you're probably ok at 19. I have one I work with right now that is 21, but looks and acts like he's in his mid-teens. Generally speaking, though, the larger the breed, the shorter their life-span. I had a 17-hand "Heinz-57" (grade) gelding die of old age at about 22. The work horse breeds are often done by 24. Then again, I once saw a 32 year-old mare toss her professional bronc rider off right between her ears at the Tucson Rodeo one year. He didn't get close to 8 seconds!
Have a vet check the horse before you lay down the money. People want to get rid of old horses because they don't want to have to feed them after their useful life or bury them when they die. They will often under-state the age of the animal. Your 19 year-old could easily be a 25 year-old. With experience, you can age a horse pretty close by their front teeth.
You should also consider the fact that after you've had this 19 year-old for 5 years, he'll be 24 and you won't be able to give him away, much less sell him. Some folks have here have said their 30+ animals are still making way, but that is not
the norm by a long shot. Most horses get "put out to pasture" or made "pasture mates" by the time they are in their mid-late 20s.
It's no different with people. Some folks jog 5 miles a day at age 70. Others, like me, have knee problems at age 54. Some folks live to be 94, others die in their 50s. Some horses develop back trouble as they age, just like people.
If I were you, I'd be looking for a horse in the 12-16 age range. They are mature, as stable as they'll ever be, and you can pick them up inexpensively just about anywhere in the country. You will be able to keep him and ride him for a good 6-10 years, if he's an average horse. If he doesn't work out, you won't have too much trouble selling or giving him away at 17-18 years-old.
Just my 2 cents. Worth about that.
Here's one you might take a look at